arXiv subjects

Zimo Sun

Publications and source records attributed to Zimo Sun.

26 records · Page 2Linked to original sources

arXiv2023

Ladder Symmetries of Black Holes and de Sitter Space: Love Numbers and Quasinormal Modes

In this note, we present a synopsis of geometric symmetries for (spin 0) perturbations around (4D) black holes and de Sitter space. For black holes, we focus on static perturbations, for which the (exact) geometric symmetries have the group structure of SO(1,3). The generators consist of three spatial rotations, and three conformal Killing vectors obeying a special melodic condition. The static perturbation solutions form a unitary (principal series) representation of the group. The recently uncovered ladder symmetries follow from this representation structure; they explain the well-known vanishing of the black hole Love numbers. For dynamical perturbations around de Sitter space, the geometric symmetries are less surprising, following from the SO(1,4) isometry. As is well known, the quasinormal solutions form a non-unitary representation of the isometry group. We provide explicit expressions for the ladder operators associated with this representation. In both cases, the ladder structures help connect the boundary condition at the horizon with that at infinity (black hole) or origin (de Sitter space), and they manifest as contiguous relations of the hypergeometric solutions.

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arXiv2023

Ginzburg-Landau Description and Emergent Supersymmetry of the $(3,8)$ Minimal Model

A pair of the 2D non-unitary minimal models $M(2,5)$ is known to be equivalent to a variant of the $M(3,10)$ minimal model. We discuss the RG flow from this model to another non-unitary minimal model, $M(3,8)$. This provides new evidence for its previously proposed Ginzburg-Landau description, which is a $\mathbb{Z}_2$ symmetric theory of two scalar fields with cubic interactions. We also point out that $M(3,8)$ is equivalent to the $(2,8)$ superconformal minimal model with the diagonal modular invariant. Using the 5-loop results for theories of scalar fields with cubic interactions, we exhibit the $6-ε$ expansions of the dimensions of various operators. Their extrapolations are in quite good agreement with the exact results in 2D. We also use them to approximate the scaling dimensions in $d=3,4,5$ for the theories in the $M(3,8)$ universality class.

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arXiv2022

Quantum de Sitter horizon entropy from quasicanonical bulk, edge, sphere and topological string partition functions

Motivated by the prospect of constraining microscopic models, we calculate the exact one-loop corrected de Sitter entropy (the logarithm of the sphere partition function) for every effective field theory of quantum gravity, with particles in arbitrary spin representations. In doing so, we universally relate the sphere partition function to the quotient of a quasi-canonical bulk and a Euclidean edge partition function, given by integrals of characters encoding the bulk and edge spectrum of the observable universe. Expanding the bulk character splits the bulk (entanglement) entropy into quasinormal mode (quasiqubit) contributions. For 3D higher-spin gravity formulated as an sl($n$) Chern-Simons theory, we obtain all-loop exact results. Further to this, we show that the theory has an exponentially large landscape of de Sitter vacua with quantum entropy given by the absolute value squared of a topological string partition function. For generic higher-spin gravity, the formalism succinctly relates dS, AdS$^\pm$ and conformal results. Holography is exhibited in quasi-exact bulk-edge cancelation.

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arXiv2021

A note on the representations of $\text{SO}(1,d+1)$

$\text{SO}(1, d+1)$ is the isometry group of $(d+1)$-dimensional de Sitter spacetime $\text{dS}_{d+1}$ and the conformal group of $\mathbb{R}^{d}$. This note gives a pedagogical introduction to the representation theory of $\text{SO}(1, d+1)$, from the perspective of de Sitter quantum field theory and using tools from conformal field theory. Topics include (1) the construction and classification of all unitary irreducible representations (UIRs) of $\text{SO}(1,2)$ and $\text{SL}(2,\mathbb R)$, (2) the construction and classification of all UIRs of $\text{SO}(1,d+1)$ that describe integer-spin fields in $\text{dS}_{d+1}$, (3) a physical framework for understanding these UIRs, (4) the definition and derivation of Harish-Chandra group characters of $\text{SO}(1,d+1)$, and (5) a comparison between UIRs of $\text{SO}(1, d+1)$ and $\text{SO}(2,d)$.

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arXiv2020

AdS one-loop partition functions from bulk and edge characters

We show that the one-loop partition function of any higher spin field in $(d+1)$-dimensional Anti-de Sitter spacetime can be expressed as an integral transform of an $\text{SO}(2,d)$ bulk character and an $\text{SO}(2,d-2)$ edge character. We apply this character integral formula to various higher-spin Vasiliev gravities and find miraculous (almost) cancellations between bulk and edge characters that lead to agreement with the predictions of HS/CFT holography. We also discuss about the relation between the character integral representation and Rindler-AdS thermal partition function.

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arXiv2020

Higher spin de Sitter quasinormal modes

We construct higher spin quasinormal modes algebraically in $D$-dimensional de Sitter spacetime using the ambient space formalism. The quasinormal modes fall into two nonunitary lowest-weight representations of $\mathfrak{so}(1, D)$. From a local QFT point of view, the lowest-weight quasinormal modes of massless higher spin fields are produced by gauge-invariant boundary conserved currents and boundary higher-spin Weyl tensors inserted at the southern pole of the past boundary. We also show that the quasinormal spectrum of a massless/massive spin-$s$ field is precisely encoded in the Harish-Chandra character corresponding to the unitary massless/massive spin-$s$ $\text{SO}(1, D)$ representation.

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arXiv2017

Higher genus Siegel forms and multi-center black holes in N=4 supersymmetric string theory

We conjecture that the Fourier coefficients of a degree three Siegel form, $1/\sqrt{χ_{18}}$, count the degeneracy of three-center BPS bound states in type II string theory compactified on $K3 \times T^2$. We provide evidence for our conjecture in the form of consistency with physical considerations of wall-crossing, holographic bounds, and the appearance of suitable counting functions (involving the inverse of the modular discriminant $Δ$ and the inverse of the Igusa cusp form $Φ_{10}$) in limits where the count degenerates to involve single-center or two-center objects.

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arXiv2017

Higher Spin de Sitter Hilbert Space

We propose a complete microscopic definition of the Hilbert space of minimal higher spin de Sitter quantum gravity and its Hartle-Hawking vacuum state. The fundamental degrees of freedom are $2N$ bosonic fields living on the future conformal boundary, where $N$ is proportional to the de Sitter horizon entropy. The vacuum state is normalizable. The model agrees in perturbation theory with expectations from a previously proposed dS-CFT description in terms of a fermionic Sp(N) model, but it goes beyond this, both in its conceptual scope and in its computational power. In particular it resolves the apparent pathologies affecting the Sp(N) model, and it provides an exact formula for late time vacuum correlation functions. We illustrate this by computing probabilities for arbitrarily large field excursions, and by giving fully explicit examples of vacuum 3- and 4-point functions. We discuss bulk reconstruction and show the perturbative bulk QFT canonical commutations relations can be reproduced from the fundamental operator algebra, but only up to a minimal error term $\sim e^{-\mathcal{O}(N)}$, and only if the operators are coarse grained in such a way that the number of accessible "pixels" is less than $\mathcal{O}(N)$. Independent of this, we show that upon gauging the higher spin symmetry group, one is left with $2N$ physical degrees of freedom, and that all gauge invariant quantities can be computed by a $2N \times 2N$ matrix model. This suggests a concrete realization of the idea of cosmological complementarity.

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